There have been many suggestions for mass drivers on Luna for the exportation of raw materials and other purposes, notably by Gerard K. O'Neill (God rest his soul) and the Space Studies Institute. Plans can keep the power requirement low by calling for a low payload size. Higher acceleration rates allow shorter track. High firing rates keep the investment actively earning its return.
Circum Polar Mass Driver
Consider here a circular mass driver or mass accelerator which would keep power requirements low by spreading the acceleration out over many laps of a circular track. The payload could be about 200 kilograms. If there are passengers or cargo available every 110 minutes for rendezvous with a catcher satelite, it can keep constantly busy. Suitability for passenger service requires a low radial acceleration, 30 meters per second squared (about 3 g's) will do. This in turn requires a large diameter (about 120 miles). The shape of the device is like a very regular volcanic mountain peak with gently sloping sides and a circular crater on top. The accelerator track would run along the vertical wall of the circular crater. When the payload and carrier reach orbital velocity (1680 meters per second), the payload is dropped tangentially outward over the top of the wall. A counter weight may be required on the carrier near the base of the wall to ballance the carrier. Since the diameter of the track is 120 miles, there is about one and two thirds miles bulge of the curvature of Luna interfering with line of sight communication from one side of the track to the other. The plane of the circular track makes a 3.2 degree angle with the surface of Luna. (It's like a slice off of the top of Luna one and two thirds miles thick at the Pole.) Payloads launched tangentialy from the track, however, deviate from that plane by curving downward toward Luna in an orbital path. This makes it more likely than otherwise that a payload would smash into a mountain peak. So the accelerator track should be built up on fill as high as practical and care should be taken in choosing the exact dirrection of launch. The circular accelerator should be centered at the North pole while the catcher satelite would orbit about once per 110 minutes at an inclination of about 86.8 degrees. So it would pass over one or another spot on the circular track with every orbit as Luna rotates under the orbit. It could catch a payload whenever a mountain peak did not interfere. Troublesome peaks could be razed.
The above specifications would require 43 kilowatts average power put constantly into payloads plus power to accelerate the carrier and allow for the losses in magnetic levitation. Unfortunately, the carrier can not constantly accelerate because it must come to a stop to be ready to pick up the next payload. Two tracks, the second with 10 meters less radius and 2 meters more altitude than the first would allow one track to accelerate while the other uses regenerative braking.
As long as we consider developments that must be many years in the future, there is a capability of adding carriers in a train as there is increased available power and need for cargo tonnage. The whole 370 mile circumference of the accelerator could be filled with one train of carriers. The payloads could be connected by rope and the whole train of payloads launched from one point on the cicumference into one orbit as 5 minutes and 53 seconds go by.
The First Lunar Mass Driver
Catching one kilogram loads of sintered soils at L2 one a second or one every few seconds by having them smash into a grid and having the bits go through to fill up a cone is unacceptable. A continuing rain of dust and grit would be produced at L2 from whence it would fill up the plane of the Earth Luna system and trail a cloud into independent orbit around the sun.  The dust from thousands of tons of stuff splashed into a catcher would sandblast every satelite in orbit.
What Will Work
Instead a mass driver should launch 10 kilogram loads as fast as can be managed. This should be once a minute or better. The payloads should go into equatorial orbit about Luna. Each payload should be about a 10.1 kilogram spaceship containing a supposed 100 gram liquid oxygen flash baulb rocket(It has a combustion chamber stuffed with aluminum coated aluminum oxide threads. An electric pulse ignites the thermite that melts the valve to the oxygen tank open).  The payload is spin stabilized and the rocket is fired by a timer at apolune to circularize the orbit. The payloads orbit at a 111 minute orbit at 30 kilometers altitude. The catcher satelite orbits at 127 kilometers altitude once every 120 minutes. A net is depended by tether from the catcher and sweeps up the entire payload orbit once in twenty-four hours.
Previous schemes called for a mass driver built as prefabricated sections on Earth for shipping raw materials into orbit for processing. This scheme calls for the mass driver to be built from lunar materials by remote controled devices. So there will be the infrastructure for manufacturing many things by the time the mass driver comes on line. The same things that went into building the mass driver will be shipped out as export. We will let a full engineering team calculate which scheme requires more stuff shipped from earth by the time of first exports.
- The lack of a reference here has been noted and effort is underway.
- The performance characteristics of this hypothetical rocket are themselves hypothetical. See discussion for this article.